When winding a close wound coil of wire on a rotating mandrel it is known to form the wire into a coil by first guiding the wire around the mandrel and subsequently applying pressure by a pressure wheel which rotates against the mandrel so as to urge the wire against the mandrel. In order to move the coil of wire thus formed along the mandrel, the pressure wheel is formed with an inclined peripheral surface which urges the coil in the required direction. This known manner of winding a helical coil has the disadvantage of requiring pressure both to form the coil and to cause the coil to advance along the mandrel. This imposes an effective limit on the rotational speed of the mandrel of some 2,000 to 4,000 r.p.m.